Someone her age should have regular chores anyway. She should be cleaning her room as well as some routine jobs around the house (emptying dishwasher, feeding the dog, vacuuming, dusting, etc.)

Definitely teach her how to do laundry. The next time she complains, point out that she is capable of washing her own clothes. She can wash them herself, or she can wait until you get around to it. You are not going to jump to satisfy someone who is acting rudely.

OP - Does your daughter relate to her siblings in a typical fashion at least some of the time? Does she do things with peers her own age outside of school? I ask this because if she is for whatever reason a loaner and seems to be lacking in empathy and other typical reactions to other people, it might at least a mild symptom of something a bit off in social skills or interpersonal skills which might need to be addressed in some way.

Being sure that she is a member of your family unit with personal and family responsibilities is key. Also seeing that she can enjoy doing things with your family - at least some of the time and does not just want to be on her own is another thing to look out for. We had a very high performer who was very much "XX Centric," and I wished we had realized just how far it went before she went off to college.

I never experienced this with laundry, but my older kid loved to ask to be chauffeured place to place despite living walking distance to downtown SS, MD, and access to the school bus, TWO bikes (mountain and city), and a topped off Smarttrip card. I said no in the nicest way possible unless I already had to be out, conditions were nasty, or she was going to have a heavy load of books, sports equip, etc.